1919 Mercator Charts - Scale — Page 313, Lesson 281

I want to walk you through a key technique for working with Mercator chart scales. This is a topic where understanding the pattern can save you a lot of calculation time in the exam. Let me start with the first learning point. When you see scale questions in the exam, the answer options are often approximated to the nearest round number. For example, the correct answer to a scale question might be 1:3,258,538, but the closest option available might be 1:3,250,000. That rounding is not unusual — it's standard practice in these questions. Now here's the really useful insight: you don't always need to do the full calculation. On a Mercator chart, scale must expand as you move away from the Equator. That means the scale gets larger — the representative fraction gets smaller in terms of its denominator. Let me explain that carefully. The representative fraction, or RF, is written as 1:something. That "something" is the denominator. A scale of 1:2,000,000 means one unit on the chart represents 2,000,000 of the same units on the Earth. Now, a smaller scale means the denominator is larger — you're representing more Earth distance per unit of chart distance. A larger scale means the denominator is smaller. On a Mercator chart, as you move away from the Equator toward the poles, the scale expands — it gets larger. So the denominator must get smaller. Conversely, at the Equator, the scale is smallest, so the denominator is largest. Here's how you use that. If you know the denominator at 52 degrees South is 2,000,000, then the denominator at the Equator must be a bigger number — the scale must be smaller. So if you're given a set of options, and only one of them has a denominator larger than 2,000,000, that's your answer. That saves you time. Now let me give you the formula for finding the Mercator scale at one latitude when you know it at another latitude. There's a short-cut formula that avoids using secants and avoids having to write the representative fraction as a fraction. You just need to remember that the large figure in the RF is the denominator — that's the figure we most commonly remember. For example, a 1:500,000 chart, which is an ICAO topo chart, has a denominator, which we call D, of 500,000. Here's the derivation. When comparing scales at two different latitudes on a Mercator chart, we start with the relationship at each latitude. At latitude A, the scale at A equals the scale at the Equator multiplied by the secant of latitude A. At latitude B, the scale at B equals the scale at the Equator multiplied by the secant of latitude B. If we divide the two scale formulae, the scale at the Equator cancels out. So we get: scale at A divided by scale at B equals secant A divided by secant B. You don't need to memorise the derivation steps, but the final formula is important. The scale at one latitude relative to another is simply the ratio of the secants of those latitudes. And since secant is 1 over cosine, this is the same as the ratio of the cosines inverted — but the key point is that the formula lets you compare scales directly without needing the Equator scale. So to summarise: on a Mercator chart, scale expands away from the Equator, so the denominator gets smaller. And when you need to find the scale at one latitude given the scale at another, you use the ratio of secants of those latitudes. The formula is scale at A over scale at B equals secant A over secant B.